Large deviation principle for linear mod 1 transformations

17 Mar 2020 Yamamoto Yong Moo Chung ad Kenichiro

For $0\le \alpha <1$ and $\beta>2$, we consider a linear mod 1 transformation on a unit interval; $x\mapsto\beta x+\alpha$ (${\rm mod}\ 1$), and prove that it satisfies the level-2 large deviation principle with the unique measure of maximal entropy. For the proof, we use the density of periodic measures and Hofbauer's Markov Diagram...

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  • DYNAMICAL SYSTEMS